Question

A system of equations is graphed on the coordinate plane.

y=−2x−4y=2x+4

What is the solution to the system of equations?

Enter the coordinates of the solution in the boxes.

(
, ​
)

A graph of the system of equations y equals negative 2 x minus 4 and y equals 2 x plus 4.

Answer 1

To find the solution to the system of equations given by:

1. \( y = -2x - 4 \)
2. \( y = 2x + 4 \)

we can set the two equations equal to each other since they are both equal to \( y \):

\[
-2x - 4 = 2x + 4
\]

Now, let's solve for \( x \):

1. Add \( 2x \) to both sides:

\[
-4 = 4x + 4
\]

2. Subtract \( 4 \) from both sides:

\[
-8 = 4x
\]

3. Divide both sides by \( 4 \):

\[
x = -2
\]

Now that we have \( x \), we can substitute it back into either of the original equations to find \( y \). Using the second equation:

\[
y = 2(-2) + 4
\]

\[
y = -4 + 4 = 0
\]

So the solution to the system of equations is:

\[
(x, y) = (-2, 0)
\]

The coordinates of the solution are:

\[
\boxed{(-2, 0)}
\]